Simulating Many-Body Systems with a Projective Quantum Eigensolver

Understand

We present a new hybrid quantum-classical algorithm for optimizing unitary coupled-cluster (UCC) wave functions deemed the projective quantum eigensolver (PQE), amenable to near-term noisy quantum hardware.

• Contrary to variational quantum algorithms, PQE optimizes a trial state using residuals (projections of the Schr\"{o}dinger equation) rather than energy gradients.
• We show that the residuals may be evaluated by simply measuring two energy expectation values per element.
• We also introduce a selected variant of PQE (SPQE) that uses an adaptive ansatz built from arbitrary-order particle-hole operators, offering an alternative to gradient-based selection procedures.